1. Technical Field of the Invention
The present invention relates in general to measurement systems, and in particular to processing and filtering of time discrete measurement data.
2. Description of Related Art
Frequently, in monitoring and control systems, there is a need to generate estimates of a magnitude of interest from multiple instantaneous measurements. If the measuring method adds uncertainty or noise, or if noise is present in the monitoring environment, filtering of a series of measurements is needed to generate a reliable or accurate estimate. Similarly, if the measured quantity varies with time, sometimes the average value, the trend, or the long term variations of the measured quantity, rather than the instantaneous value, are of interest. To generate such an average value, trend, or long term variation, filtering of instantaneous measurements is needed.
Generally, one or more sensors are used to measure the quantity of interest. The sensors can be any measuring equipment, wherein the measurements are sampled from the sensors at regular intervals. In many cases, not all sensors deliver measurements at every sampling instant, or individual measurements might be discarded from some reason. Furthermore, each individual measurement might not be equally reliable. As a result, each measurement can have an associated reliability, which can be a function of the reliability of the particular measurement and/or the reliability of the sensor. To generate an accurate or reliable estimate of the quantity of interest, it is important to consider the reliability of each measurement during the estimation procedure.
When a time variant quantity is to be estimated, it is often desirable to rely, at least in part, on historical measurements to generate a more reliable estimate of the current quantity. Typically, measurements made recent in time are more relevant to the current estimate than earlier measurements. As a result, more recent measurements should be given more importance or weight during the estimation process. This weighting procedure can be exemplified by an estimator that gradually forgets old measurements as new measurements are received. One way to achieve this result is to use historical weights that decrease exponentially with time. Thus, if two measurements are separated by n time instants (corresponding to a time difference of txe2x88x92nT seconds, where T is the time between consecutive time instants and t is the time of the later measurement), the older of the two measurements are considered (1xe2x88x92xcex2)n times less important, where xcex2 is a parameter called the forgetting factor. The value of the forgetting factor determines how fast the estimator forgets old measurements and must be a number between 0 and 1, where values close to 1 result in an estimator that forgets quickly.
A similar situation is presented when the sensors deliver measurements of different quantities. It might then be of interest to collect the measurements on a per sensor basis, but to also average the measurements over all of the sensors. Such a situation might arise, for example, when a temperature sensor is installed in each room in a building. The filtering and averaging process should then take into account the reliability of each individual sensor and its corresponding measurement when estimating the overall temperature.
A common method of generating estimates is to filter measurements through an auto-regressive filter:
Sn=(1xe2x88x92xcex2)Sn-1+xcex2mnxe2x80x83xe2x80x83(1 )
where mn is the average of measurements over the sensors at time instant n, and Sn is the estimate of the measured quantity at time instant n. Problems arise, however, when measurements are missing, which causes the number of existing measurements to vary with time. In particular, a large number of measurements at a first time instant will not be given more weight than a small number of measurements at a second time instant. This problem is further exacerbated when no measurements exist for some sampling instants. Moreover, this filtering method does not take into account the reliability of the measurements.
A similar approach would be to filter the measurements from each sensor through separate auto-regressive filters and calculate the average of the filter outputs. This procedure, however, will suffer from the same problems as the previous method.
Another alternative might be to store historical measurements and to calculate the current estimate using both the current and historical measurements. Again, however, such a method would suffer from the same problems discussed above. Furthermore, this method would also require relatively large amounts of memory and would increase the computational complexity of the estimation procedure.
There is a need, therefore, for a method and apparatus that would filter measurements in an efficient way (i.e., with low memory requirements and low computational complexity). Preferably, such a method would provide an average of measurements over all of the sensors and would take into account historical measurements, with the weight of the historical measurements decreasing exponentially with time. Moreover, it would be desirable for the filtering method and apparatus to take into account only the existing measurements (i.e., corresponding to those sampling instants in which measurement data is received) together with an associated reliability of the measurements.
The present invention comprises an apparatus and method for recursively filtering measurement data. The apparatus and method operate to generate an unbiased average of measurements from one or more sensors. The weight of historical measurements and their corresponding reliability indicators in the unbiased average decrease exponentially with time. In addition, the apparatus and method account for measurements that are intermittent or unequally reliable.
The apparatus of the invention includes a buffer for storing measurements of a time-varying attribute that are made during a particular time instant. Each measurement has an associated reliability indicator representing a relative reliability of the measurement. The apparatus further includes a memory for storing filtering instructions, which are used to generate an estimated magnitude for the time-varying attribute at the particular time instant, and a processor for filtering the plurality of measurements in accordance with the filtering instructions. In particular, the processor operates to time-weight a historical estimated magnitude of the time-varying attribute and to generate a weighted average of the plurality of measurements using the reliability indicators associated with the plurality of measurements. Using the time-weighted historical estimated magnitude, the processor generates an estimated magnitude of the time-varying attribute for the particular time instant.
In accordance with the method of the invention, time discrete measurement data relating to a measurable time-varying attribute is filtered to generate an estimated magnitude for the attribute at a particular time instant. One or more measurements of the time-varying attribute are collected during the time instant. Each measurement has an associated reliability indicator that represents a relative reliability of said measurement. First, the reliability indicators for the measurements are filtered to produce a filtered reliability indicator, which includes a time-weighted historical reliability indicator. Then, the measurements are filtered to produce an estimated magnitude of the attribute for the current time instant. The estimated magnitude is determined using a time-weighted and reliability-weighted historical estimated magnitude of the time-varying attribute and a reliability-weighted average of the measurements. The reliability weighting of the reliability-weighted historical estimated magnitude and the reliability-weighted average of the measurements is performed using said filtered reliability indicator.